If the angel $$\theta $$ between the line $${{x + 1} \over 1} = {{y - 1} \over 2} = {{z - 2} \over 2}$$ and

the plane $$2x - y + \sqrt \lambda \,\,z + 4 = 0$$ is such that $$\sin \,\,\theta = {1 \over 3}$$ then value of $$\lambda $$ is :

If the plane $$2ax-3ay+4az+6=0$$ passes through the midpoint of the line joining the centres of the spheres

$${x^2} + {y^2} + {z^2} + 6x - 8y - 2z = 13$$ and

$${x^2} + {y^2} + {z^2} - 10x + 4y - 2z = 8$$ then a equals :

The distance between the line

$$\overrightarrow r = 2\widehat i - 2\widehat j + 3\widehat k + \lambda \left( {i - j + 4k} \right),$$ and the plane

$$\overrightarrow r .\left( {\widehat i + 5\widehat j + \widehat k} \right) = 5$$ is

The angle between the lines $$2x=3y=-z$$ and $$6x=-y=-4z$$ is :